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# Online Undergraduate Research Seminar – Prof. Peter McGrath (NCSU) and Mathew Kushelman

## October 10, 2023 @ 3:00 pm - 4:00 pm

**On Liouville’s theorem for conformal maps**

**Abstract**. A theorem of Liouville asserts that the simplest conformal transformations on Euclidean space—translations, dilations, reflections, and inversions—generate all conformal transformations when the dimension is at least 3. I will describe a new proof of this theorem which is shorter and more elementary than the argument, due to Nevanlinna, found in most modern textbooks.